Graph f(x)=x^2-8x+15

Graph f(x)=x^2-8x+15
Find the properties of the given parabola.
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Rewrite the equation in vertex form.
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Complete the square for .
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Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
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Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Find the value of using the formula .
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Simplify each term.
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Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Subtract from .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Use the vertex form, , to determine the values of , , and .
Since the value of is positive, the parabola opens up.
Opens Up
Find the vertex .
Find , the distance from the vertex to the focus.
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Find the distance from the vertex to a focus of the parabola by using the following formula.
Substitute the value of into the formula.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Find the focus.
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The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Substitute the known values of , , and into the formula and simplify.
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
Find the directrix.
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The directrix of a parabola is the horizontal line found by subtracting from the y-coordinate of the vertex if the parabola opens up or down.
Substitute the known values of and into the formula and simplify.
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
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Subtract from .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
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Subtract from .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
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Subtract from .
Add and .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
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Subtract from .
Add and .
The final answer is .
The value at is .
Graph the parabola using its properties and the selected points.
Graph the parabola using its properties and the selected points.
Direction: Opens Up
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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Name

Name four hundred seventy-five million two hundred forty-five thousand forty-four

Interesting facts

  • 475245044 has 16 divisors, whose sum is 1115792928
  • The reverse of 475245044 is 440542574
  • Previous prime number is 23

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 35
  • Digital Root 8

Name

Name four hundred five million five hundred sixteen thousand seven hundred eighty

Interesting facts

  • 405516780 has 64 divisors, whose sum is 1056097440
  • The reverse of 405516780 is 087615504
  • Previous prime number is 53

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 36
  • Digital Root 9

Name

Name one billion six hundred eight million fifty-seven thousand seven hundred sixty-six

Interesting facts

  • 1608057766 has 16 divisors, whose sum is 2775175200
  • The reverse of 1608057766 is 6677508061
  • Previous prime number is 149

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 46
  • Digital Root 1